Recent years have seen a growing trend of learning random fields using machine learning models, including but not limited to:
Gaussian Processes [1]},
Bayesian neural networks [2]},
and most recently, generative models [3]}.
Among the generative models, generative adversarial networks (GAN) have demonstrated its robustness in various applications, from image or video generation [4]} to uncertainty quantification (UQ) [5]}.
For UQ problems, physics-informed GANs (PhysGAN) is becoming increasingly popular to quantify uncertainty in stochastic differential equations [6]}, [3]}, [8]}, [9]}. Little research, though, has been documented when randomness inherently arises from human behaviors or inherent dynamics.
In other words, the existing literature on PhysGAN integrates a deterministic physics model into GANs because it is assumed that the equations that generate data are deterministic and the prediction contains stochasticity due to randomness from initial or boundary conditions.
In this paper, in contrast, we will assume that the models that generate data are themselves stochastic due to randomness in parameters, and thus, stochastic physics models need to be integrated to capture the randomness from these sources.
